Involutory and invertible fuzzy BCK-algebras
A fuzzy ideal \(\mu\) of a commutative BCK-algebra \(X\) is said to be involutory if \(\mu^{++}=\mu\), where \(\mu^+ (x)=1-\inf\{\mu(y) |y\wedge x=0\}\). In bounded implicative BCK-algebras all fuzzy ideals are involutory. Moreover, if in a commutative BCK-algebra \(X\) all fuzzy ideals are involutory and \(\mu^+\) is a fuzzy ideal for every fuzzy ideal \(\mu\), then the set of all fuzzy ideals of \(X\) is a distributive lattice with respect to the fuzzy operations \(\cup\) and \(\cap\).
scientific article; zbMATH DE number 1563552